MRI systems are commonly used to obtain an interior image from a patient for a particular region of interest that can be used to determine the health of the patient. MRI systems include a main magnet assembly for providing a strong uniform main magnetic field to align the individual magnetic moments of the 1H atoms within the patient's body. During this process, the 1H atoms oscillate around their magnetic poles at their characteristic Larmor frequency. If the tissue is subjected to an additional magnetic field, which is tuned to the Larmor frequency, the 1H atoms absorb additional energy, which rotates the net aligned moment of the 1H atoms. The additional magnetic field is typically provided by an RF excitation signal. When the additional magnetic field is removed, the magnetic moments of the 1H atoms rotate back into alignment with the main magnetic field thereby emitting an NMR signal. The NMR signal is received and processed to form an MRI scan or image. The MRI scan is based on the distribution of 1H atoms within the body. Bodily fluids have the highest density of 1H atoms, followed by soft tissues, then cartilage and then membranes.
If the main magnetic field is uniform across the entire body of the patient, then the RF excitation signal will excite all of the 1H atoms in the sample non-selectively. Accordingly, in order to image a particular portion of the patient's body, magnetic field gradients Gx, Gy and Gz in the x, y and z directions, having a particular timing, frequency and phase, are superimposed on the uniform magnetic field such that the RF excitation signal excites the 1H atoms along a desired slice of the patient's body and unique phase and frequency information is encoded in the NMR signal depending on the location of the 1H atoms along the “image slice”. Gradient magnets are switched on to provide the gradient magnetic fields Gx, Gy and Gz. The frequencies in the NMR signal come from different locations in the selected slice, while the signal strength reveals the density of the 1H atoms. The frequencies in the NMR signal also depend on the strength of the local magnetic field produced by the combination of the uniform magnetic field and the gradient magnetic fields at the selected slice.
Typically, portions of the patient's body to be imaged are scanned by a sequence of measurement cycles in which the magnetic field gradients Gx, Gy and Gz vary according to the particular MRI imaging protocol that is being used. For each MRI scan, the resulting NMR signals are digitized and processed to reconstruct the image in accordance with the MRI imaging protocol that is used, many of which are well known to those skilled in the art.
In MRI systems, two important parameters are the time required to obtain MRI data to produce the medical images and the quality of the medical images. Reduction in data acquisition time is important, since reduced imaging time can result in improved image quality by reducing the chance that a motion artifact occurs, improve patient comfort since some patients experience claustrophobia when placed in the imaging device, and increase the number of patients that can be tested in a given time period. A reduction in imaging time also enables the performance of specialized medical test procedures such as functional MRI tests. An increase in image quality allows for more accurate interpretation and diagnosis of any health issues that the patient may have.
To reduce data acquisition time, various techniques have been proposed for sampling the NMR signal. The data acquired from the NMR signal is referred to as k-space data which is a two-dimensional data set. The k-space data provides frequency and phase information from which an MRI image is produced via application of the inverse 2D Fourier Transform, for example. The manner in which the NMR signal is generated and sampled to provide the 2D k-space data is referred to as a k-space trajectory. Different k-space trajectories confer different properties on the reconstructed MRI image.
One example of a k-space trajectory is a polar k-space trajectory in which data is acquired in a coordinate system that is described by radial (r) and azimuthal (θ) variables. The most common polar trajectories are spiral [1] and projection-reconstruction (PR) [2] k-space trajectories. Polar trajectories can generate high-quality images from undersampled data [3]. This is accomplished by employing a variable-density sampling strategy which undersamples the outer regions of k-space while maintaining a sufficient density in the inner region. Since only the low-intensity outer k-space data experiences aliasing, the intensity of the resulting artifact in the reconstructed image is low [4,2].
Generally, in a fixed data acquisition time, undersampling the k-space data by varying the k-space trajectory provides a means for trading off improved spatial resolution versus increased artifact. However, one drawback with existing polar trajectories is a limited ability to vary the sampling density, and thus alter the parameters of the resolution-artifact tradeoff. For instance, the spiral k-space trajectory can only be varied in the radial direction, while the PR k-space trajectory can only be varied in the azimuthal direction. Additionally, the PR k-space trajectory always varies at a fixed rate proportional to 1/r. This limited flexibility in varying the k-space trajectory restricts one's ability to alter, and thus optimize, the parameters of the resolution-artifact tradeoff.